Derivative of 3cosx

Derivative of 3cosx

Derivative
d/dx(3 cos(x)) = -3 sin(x)
Alternate form
3/2 i e^(i x) – 3/2 i e^(-i x)
Roots
x = pi n, n element Z
Series expansion at x=0
-3 x + x^3/2 – x^5/40 + O(x^6)
(Taylor series)
Indefinite integral
integral -3 sin(x) dx = 3 cos(x) + constant
Global minima
min{-3 sin(x)} = -3 at x = 2 pi n + pi/2 for integer n
Definite integral over a half-period
integral_0^pi-3 sin(x) dx = -6
Definite integral mean square
integral_0^(2 pi) (9 sin^2(x))/(2 pi) dx = 9/2 = 4.5

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